Spherically symmetric static vacuum solutions have been built in f (T ) models of gravity theory. We apply some conditions on the metric components; then the new vacuum spherically symmetric solutions are obtained. Also, by extracting metric coefficients we determine the analytical form of f (T ).
We study the static cosmological solutions and their stability at background level in the framework of massive bigravity theory with Friedmann-Robertson-Walker (FRW) metrics. By the modification proposed in the cosmological equations subject to a perfect fluid we obtain new solutions interpreted as the Einstein static universe. It turns out that the non-vanishing size of initial scale factor of Einstein static universe depends on the non-vanishing three-dimensional spatial curvature of FRW metrics and also the gravitons mass. By dynamical system approach and numerical analysis, we find that the extracted solutions for closed and open universes can be stable for some viable ranges of equation of state parameter, viable values of fraction of two scale factors, and viable values of graviton's mass obeying the hierarchy m << MP l which is more cosmologically motivated.
In a Friedmann-Robertson-Walker (FRW) space-time background we study the
classical cosmological models in the context of recently proposed theory of
nonlinear minimal massive bigravity. We show that in the presence of perfect
fluid the classical field equations acquire contribution from the massive
graviton as a cosmological term which is positive or negative depending on the
dynamical competition between two scale factors of bigravity metrics. We obtain
the classical field equations for flat and open universes in the ordinary and
Schutz representation of perfect fluid. Focusing on the Schutz representation
for flat universe, we find classical solutions exhibiting singularities at
early universe with vacuum equation of state. Then, in the Schutz
representation, we study the quantum cosmology for flat universe and derive the
Schrodinger-Wheeler-DeWitt equation. We find its exact and wave packet
solutions and discuss on their properties to show that the initial singularity
in the classical solutions can be avoided by quantum cosmology. Similar to the
study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de
Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass
of graviton predicted by quantum cosmology of the minimal massive bigravity is
large at early universe. This is in agreement with the fact that at early
universe the cosmological constant should be large.Comment: 13 pages, 6 figures, published online, Phys. Lett. B (2016
We generalize the scalar tensor bigravity models to the non-minimal kinetic coupling scalar tensor bigravity models with two scalar fields whose kinetic terms are non-minimally coupled to two Einstein tensors constructed by two metrics. We show that a broad class of expanding universes can be explained by some solutions of this model. Then, we study the stability issue of the solutions by means of imposing homogeneous perturbation on the equations of motion and extract the stable solutions.
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